Field of the Disclosure
The present disclosure relates to a method of calculating a spindle rotation number capable of suppressing regenerative chatter vibration in cutting using a machine tool, a method of informing the spindle rotation number, a spindle rotation number controlling method, and an NC program editing method, and apparatus for performing these methods.
Background of the Disclosure
It has conventionally been well known that machining accuracy (in particular, surface accuracy) deteriorates due to chatter vibration when machining a workpiece using a machine tool. Such chatter vibration is roughly classified into forced chatter vibration and self-excited chatter vibration, and it has been considered that forced chatter vibration occurs when an excessive external force is applied or when a frequency of an external force is synchronized with a resonant frequency of a vibrating system. On the other hand, self-excited chatter vibration includes regeneration type chatter vibration (regenerative chatter vibration) and mode-coupling type chatter vibration, and it has been considered that regenerative chatter vibration is caused by continuing cutting in which periodic variation of cutting resistance and periodic variation of thickness of cut are increased by interaction between them (the so-called “regeneration effect”) and it has been considered that mode-coupling type chatter vibration is caused by the fact that vibration modes in two directions are coupled together when their resonant frequencies are close to each other.
Further, conventionally, as a method of suppressing regenerative chatter vibration, which is one of the above-mentioned various type of chatter vibration, there has been proposed a method in which a stability limit diagram (diagram showing a stability limit in width of cut with respect to spindle rotation number; width of cut=depth of cut) as shown in FIG. 4(a) is obtained and a spindle rotation number is adjusted so that it is positioned in a stable area. Further, a machining data correction method that is an improvement of the method is disclosed in Japanese Unexamined Patent Application Publication No. 2013-43240.
As shown in FIG. 4(a), in the stability limit diagram, there are a plurality of areas called stable pockets (for example, a “stable pocket 1”, a “stable pocket 2”, and a “stable pocket 3”) where no regenerative chatter vibration occurs even if the depth of cut is large, and spindle rotation numbers around the stable pockets are regarded as stable spindle rotation numbers. Further, when a natural frequency of a tool is represented by fr [Hz] and the number of teeth of the tool is represented by N, a spindle rotation number n1 [min−1] at the “stable pocket 1”, which is the largest spindle rotation number, is represented as n1=fr×60/N, a spindle rotation number n2 at the “stable pocket 2” is represented as n2=fr×60/(N×2), and a spindle rotation number n3 at the “stable pocket 3” is represented as n3=fr×60/(N×3). Thus, a spindle rotation number nm at a “stable pocket m” which is the mth stable pocket is represented as nm=fr×60/(N×m) (m is a positive integer). Further, the higher the spindle rotation number is, the wider the stable area of the stable pocket is.
A basic method of obtaining the stability limit diagram is explained in detail in Eiji Shamoto, “Mechanism and Suppression of Chatter Vibrations in Cutting”, Electric Furnace Steel, Vol. 82 No. 2, 2011, and Norikazu Suzuki, “Chatter Vibration in Cutting, Part 1”, Journal of the Japan Society for Precision Engineering, Vol. 76, No. 3, 2010. According to the Shamoto and Suzuki publications, a stability limit in depth of cut alim is calculated by the following equation.alim=−1/(2Kf×G(ωc))It is noted that, in the equation, Kf is a specific cutting resistance [N/mm2], G(ωc) is a real part of a compliance transfer function (ratio of vibration displacement output to force input) of a machine structure, and ωc is an angular frequency.
Further, the specific cutting resistance Kf is a force in a cutting direction when cutting a workpiece so that a chip with the thickness of 1 mm and the cross-sectional area of 1 mm2 is produced. For example, as disclosed in Japanese Unexamined Patent Application Publication No. 2013-43240, the specific cutting resistance Kf can be calculated from a value of current flowing through a spindle motor when performing a test cutting on an appropriate workpiece using a tool to be used.
Further, the real part G(ωc) of the compliance transfer function is obtained by attaching a vibration detector (acceleration sensor) to a tip end of a tool attached to a spindle of a machine tool and then striking the tip end portion of the tool with an impact hammer having a force sensor (load cell) attached to its striking portion, and processing the resultant output signal of the acceleration sensor (signal relating to free vibration of the tool) and output signal of the force sensor (signal relating to the striking force) using a dedicated processor, which is summarized and disclosed also in Japanese Unexamined Patent Application Publication No. 2013-43240.